Surface Areas & Volumes | Exercise 13.3 | Q8

Question 8: A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of the painting is Rs.12 per m², what will be the cost of painting all these cones? (Use π = 3.14 and take √1.04 = 1.02)

Video Explanation

Explanatory Answer | Exercise 13.3 Question 8

Given Data: Height of the conical barricade, h = 1 m = 100 cm
Diameter of the conical barricade, d = 40 cm
∴ Radius of the conical barricade, r = \\frac{40}{2}) = 20 cm (or) 0.2 m

Step 1: Compute Slant Height of Cone

Square of slant height of the cone , l² = h² + r²
l² = 20² + 100²
l² = 400 + 10,000 = 10400
l² = = 10,000 × 1.04
So, slant height, l = 100 (√ 1.04)
l = 100 × 1.02 = 102 cm (or) 1.02 m

Step 2: Compute Curved Surface Area of Cone and that of 50 Conical Barricades

Curved surface area of the conical barricade = π × r × l
Take π = \\frac{22}{7})
= 3.14 × 0.2 × 1.02
= 0.64056 m²

Curved surface area of 50 conical barricade = 0.64056 × 50
= 32.028 m²

Step 3: Compute Cost of Painting All Conical Barricades

Cost of painting 50 conical barricades at Rs.12 per m² = 12 × 32.028
= Rs.384.336

Exercise 13.1 | Surface Area of Cubes & Cuboids

1. Class 9 Exercise 13.1 Question 3 | Height of hall ▶
2. Class 9 Exercise 13.1 Question 6 | TSA of Herbarium ▶
3. Class 9 Exercise 13.1 Question 7 | Shanti Sweets ▶

Exercise 13.2 | Surface Area of Cylinders

1. Class 9 Exercise 13.2 Question 3 | CSA TSA of Metal Pipe ▶
2. Class 9 Exercise 13.2 Question 4 | Roller & Playground ▶
3. Class 9 Exercise 13.2 Question 9 | Cylindrical Petrol Tank ▶
4. Class 9 Exercise 13.2 Question 10 | CSA of Decorative Lampshade ▶

Exercise 13.3 | Surface Area of Cones

1. Class 9 Exercise 13.3 Question 5 | Length of Tarpaulin 3 m wide ▶
2. Class 9 Exercise 13.3 Question 8 | Cost of painting conical barricades ▶

Exercise 13.4 | Surface Area of Spheres & Hemispheres

1. Class 9 Exercise 13.4 Question 8 | Outer CSA of hemispherical bowl ▶
2. Class 9 Exercise 13.4 Question 9 | Surface area of sphere & Cylinder ▶